Notice that the graph of f(x) includes the point (10,1), after applying each listed transformation to (10,1), we get
[tex]\begin{gathered} (10,1)\rightarrow(10-2,1)=(8,1)\rightarrow\text{ 2 units to the left} \\ (10,1)\rightarrow(10-10,1)=(0,1)\rightarrow10\text{ units to the left} \\ (10,1)\rightarrow(10,-1)\rightarrow\text{ reflection over the x-axis} \\ (10,1)\rightarrow(-10,1)\rightarrow\text{ reflection over the y-axis} \\ \end{gathered}[/tex]
Thus, g(x) is a reflection across the y-axis of f(x).
The answer to 7) is option D.
8)
In general, a reflection across the y-axis is given by the transformation below
[tex](x,y)\rightarrow(-x,y)[/tex]
Therefore, in our case,
[tex]g(x)=f(-x)=log(-x)[/tex]
The answer is g(x)=log(-x), option C.
